[bengt b. broms] lateral resistance of pile

8/15/2019 [Bengt B. Broms] Lateral Resistance of Pile

1/37

3325

March,

1964

SM

2

Journal

of

the

SOIL

MECHANICS

AND

FOUNDATIONS

DIVISION

Proceedings

of.

the American

Society

of

Civil

Engineers

LATERAL

RESISTANCE OF

PILES

IN

COHESIVE SOILS

By

Bengt

B.

BromsJ

M.

ASCE

SYNOPSIS

Methods are

presented

for the

calculation

of

the ultimate

lateral

resist¬

ance

and

lateral

deflections at

working

loads of

single

piles

and pile

groups

driven

into

saturated

cohesive

soils.

Both

free and fixed headed

piles

have

been

considered.

The

ultimate lateral

resistance

has

beencalculated assuming

that failure

takes

place

either

when one

or

two

plastic

hinges

form along

each

individual pile or

when

the

lateral

resistance

of the supporting

soil

is

ex¬

ceeded

along

the total

length

of

the

laterally

loaded

pile.

Lateral

deflections

at

working

loads

have

been calculated

using

the

concept of

subgrade

reaction

taking into account

edge

effects

both

at

the

ground

surface

and at

the

bottom

of

each

individual pile.

The

results

from

the

proposed

design

methods

have been

compared

with

available test

data.

Satisfactory agreement

has

been

found between

measured

and calculated

ultimate lateral

resistance

and between

calculated

and

meas¬

ured deflections

at

working

loads.

For

design

purposes,

the

proposed

analyses

should

be

used

with caution

due

to

the

limited amounts of test

data.

;

Note.—

Discussion open

until

August

1,

1964.

To

extend

the

closing

date

one

month,

ÿ

a written

request

must

be

filed

with

the

Executive

Secretary,

ASCE.

This

paper

la

part

[

of

the copyrighted

Journal of the

Soil Mechanlos

and

Foundation* Division,

Proceedings

r

of

the

American Society

of Civil

Engineers,

Vol. 90,

No.

SM2,

March,

1964.

l

1

Assoc.

Prof,

of

Civ.

Engrg., Cornell Univ.,

Ithaca,

N.

Y.

t

27

I

i

i

l


2/37

28

March,

1964

SM

2

INTRODUCTION

Single

pileB

and pile

groups are

frequently

subjected

to

high

lateral

forces.

These

forces

may be

caused

by

earthquakes,

by wave

or wind

forces

or by

lateral

earth pressures.

For

aiample,

structures constructed

off-shore,

in

the

Gulf of

Mexico,

the

Atlantic or Pacific

Oceans,

are

subjected

to the

lateral

forces

caused

by waves

and

wind.

2

The safety

of

these

structures

depends

on

the

ability of

the

supporting

piles

to resist

the

resulting

lateral

forces.

Structures

built

in

such areas

as

the

states

of

California,

Oregon,

and

Washington,

or

in

Japan,

may

be subjected to high

lateral

accelerations

caused

by earthquakes

and the supporting

piles

are called upon

to resist the

resulting

lateral

forces.

For example,

the

building

codes

governing the

design

of structures

in

these

areas

specify frequently

that the piles

supporting

such

structures

should

have

the

ability

to

resist

a

lateral

force equal

to

10%

of

the

applied

axial

load.

3,4

Pile

supported

retaining

walls,

abutments

or lock

structures

frequently

resist

high

lateral

forces.

These

lateral

forces

may

be

caused

by

lateral

earth

pressures acting on

retaining

walls or

rigid

frame

bridges,

by

differ¬

ential fluid pressures

acting

on

lock

structures

or

by

horizontal

thruBt

loads

acting on

abutments of

fixed or

hinged

arch

bridges.

The

lateral bearing

capacity

of

vertical

piles

driven into cohesive

and

coheslonless

soils

will

be investigated

in

two papers.

This

paper is

the

first

in

that series

and

is

concerned with the lateral resistance

of

piles

driven

into cohesive

soils.

Methods will

be

presented

for

the

calculation of lateral

deflections,

ultimate

lateral

resistances

and

maximum

bending

moments

in

that

order.

In the

analyses

developed

herein,

the

following

precepts

have

been

assumed:

(a)

the deflections at

working

loads of

a

laterally

loaded

pile

should

not

be so

excessive

a

a

to

impair

the proper

function

of the

member

and

that

(b)

its

ultimate

strength

Bhould be

sufficiently

high

as

to

guard

against

complete

collapse

even under the

moBt

unfortunate

combination

of

factors.

Therefore,

emphasis

has

been

placed

on

behavior

at working

loads

and

at

failure

(collapse).

The

behavior at

working

loads

has

been

analyzed

by

elastic

theory

assum¬

ing

that

the

laterally

loaded

pile

behaves

as an

ideal

elastic

member

and that

the

supporting soil

behaves as

an ideal elastic

material.

The validity

of these

assumptions

can

only

be

established

by a

comparison

with

teBt

data.

The

behavior

at

failure

(collapse)

has

been

analyzed assuming

that

the

ultimate

strength

of

the

pile

section

or the ultimate strength of

the

supporting

soil has

been

exceeded.

It

should be

noted

that

the methods developed

in

this

paper

to

predict

behavior

at

working

loads

are

not

applicable

when

local

yielding

of

the soil

or

of the

pile

material

takes place

(when

the applied load

exceeds

about

half

the ultimate

strength

of

the

loaded

member).

2

Wiegel,

R.

L.,

Beebe,

K.

E.,

and

Moon.

J.,

Ocean-Wave

Forces

on

Circular

Cy¬

lindrical

Piles,

Transactions,

ASCE,

Vol.

124,

1959,

pp.

89-113.

3

Recommended

Lateral

Force

Requirements,

Seismology

Committee,

Structural

EngrB. Assoc.,

San

Francisco,

Calif.,

July, 1959.

4

Uniform Building

Code,

Pacific

Coast

Bldg. Officials

Conf., Los Angeles,

CalLf.,

1960.


3/37

gM

2

PILE RESISTANCE

29

BEHAVIOR

OF

LATERALLY

LOADED PILES

A

large

number

of

lateral

load testa

have

been

carried

crut on piles

driven

into

cohesive

soils.

5-27

5

Bergfelt,

A.,

The

Axial

and

Lateral

Load Bearing

Capacity, and

Failure by

Buck¬

ling

of

Piles

in

Soft

Clay,

Proceedings,

Fourth

Internatl.

Coof.

on

Soil

Mechanics

and

Foundation

Engrg., Vol.

II , London,

England

1957, pp.

8-13.

®

Browne,

W.H.,

Testa

of

North

Carolina

Poles

for

Electrical

Distribution

Lines,

North

Carolina

State

College

of

Agriculture

and

Engineering

Experiment

Station

Bul¬

letin.

No.

3,

Raleigh,

North Carolina

August,

1929.

'

Evans,

L.

T., Bearing

PUeB Subjected

to

Horizontal Loads,

Symposium on Lat¬

eral

Load

Tests

on

Piles,

ASTM

Special

Technical Publication,

No.

154, 1853,

pp. 30-35.

8

Usui,

R. D., Model

S tudy o f

a

Dynamically

Laterally

Loaded

Pile,

*

Jpurmi

of the

Soil

Mechanics

and

Foundations

Division,

ASCE, Vol.

84,

No.

SMI,

Proc.

Paper

1536,

February,

1958.

9

Krynlne,

D.

P.,

Land Slides

and

Pile

Action,

Engineering News

Record,

Vol. 107,

November,

1931,

p.

860.

10

Lazard, A.,

Moment limits

de

renversement de

fondatlons

cyllndriques

et

parallel6-plpediques

Isoldes,

AnnaleB

de llnstltute Technique

du

Bailment

et

das

Travaux

Publics,

January,

Paris,

France

1955,

pp.

82-110.

1

1

Lazard, A., Discussion, Annales

de l'lnstltute

Technique du

Bailment

et

dea

Travaux

PubllcB,

July-August,

Paris,

Franoe

1955,

pp.

786-788.

12

Lazard,

A.,

and

Gallerand, G.,

Shallow

Foundations,

Proceedings, Fifth Inter¬

natl. Conf.

on

Soil Mechanics

and

Foundation

Engrg.,

Vol.

HI,

Paris,

France

1961,

pp.

228-232.

10

Lorenz,

H.,

Zur

Tragfflhlgkelt

starrer

Spundwfinde und

Maatgrflndungen,

Bau

tec

hnlk-

Archly,

Heft 8,

Berlin,

Germany

1952,

pp.

79-82.

1*

Matlock,

H.,

and

Rlpperger,

E.

A., Procedures and

Instrumentation

for Testa

on

a

Laterally

Loaded Pile, Proceedings,

Eighth

Texas

Conf.

on

Soil

Mechanics

and

Foundation

Engrg.

Research,

Univ.

of

Texas,

Austin,

Tex.,

1950.

15

Matlock, H.,and

Rlpperger,

E.A.,

Measurement

of

Soil Pressure

on

a Laterally

Loaded Pile,

Proceedings, Amer.

Soc.

of Testing

Materials,

Vol. 58,

1958,

pp.

1245-

1259.

16

McCammon, G.

A.,

and

Ascherman,

J. C., Resistance

of Long

Hollow Plies to

Applied

Lateral Loads,

Symposium on Lateral

Load

Tests

on Piles,

ASTM Special

Tectolcal

Publication,

No.

154,

1953,

pp.

3-9.

17

McNulty,

J.

F., Thrust

Loadings

on

Piles,

Journal of

the Soil

Mechanics

and

Foundations

Division,

ASCE,

Vol.

82, No.

SM2, Proc.

Paper

940,

April,

1958.

18

Osterberg,

J.

O., Lateral

Stability

of

Poles

Embedded

In

a

Clay

Soli,

North¬

western

University

Project

208, Bell

Telephone

Labs.,

Evanston,

111.,

December,

1958.

19

Parrack,

A.

L.,

An

Investigation of

Lateral

Loads on

a

Test

Pile,

Texas

AIM

Research

Foundation,

Research

Foundation

Project

No.

31,

College

Station,

Texas

August,

1952.

20

peck,

R.

B.,

and

Ireland,

H. O., Full-Scale

Literal

Load

Test

of a

Retaining

Wall

Foundation,

Fifth

Internatl,

Conf,

on

Soil

Mechanics

and

Foundation

Engrg.,

Paris,

France,

Vol.

ET,

1961,

pp. 453-458.

21

Peck, R.

B.,

and

Davisaon,

M. T .,

discussion

of

Design

and

Stability

Consider¬

ations

for

Unique

Pier, by

James

Mlchalos

and David

P.

BLllington,

Transactions,

ASCE,

Vol.

127,

Part IV ,

1962,

pp.

413-424.

22

Sandeman,

J. W.,

Experiments on the

Resistance

to

Horizontal Stress

of

Timber

Piling,

von

Nostrand's

Engineering

Magazine,

Vol.

XXHI, 1880, pp.

493-497.

23

Seller,

J.

E.,

Effect

of

Depth

of

Embedment

on

Pole

Stability,

Wood

Preserving

News.

Vol.

10 , No.

11, 1932,

pp. 152-161,

167-168.

24

Shllts, W.

L.,

Graves,

L.

D.,

and Driscoll,

C. G.,

A Report

of

Field and

Labora¬

tory

Tests on the

Stability of

Posts

Against

Lateral

Loads,

Proceedings,

Second

Inter¬

natl. Conf. on

Soli

Mechanics

and

Foundation

Engrg.,

Rotterdam,

Holland

Vol.

V,

1948

p.

107.

25

Terzaghl,

K., Theoretical

Soil

Mechanics,

John

Wiley

&

Sons, Inc.,

New

York,

N.

Y.,

1943.


4/37

'•0

March,

1964

SM 2

In

many

cz#em

the

available

data

are difficult

to

interpret.

Frequently,

load

tests have

been carried

out

for

the

purpose

of

proving

to

the

satisfaction

of

the

owner

or the

design

engineer

that

the

load

carrying

capacity

of

a

pile

or

a pile

group

is

sufficiently

Large

to resist

a

prescribed

lateral

design

load

Under

a specific

condition.

In

general,

sufficient data

are

not

available

con¬

cerning the

strength

and

deformation

properties,

the

average relative

density

and

the angle

of

internal

friction

of

cohesionless

soils or

the average ubcon-

fined

compressive

strength

of

the

cohesive

soil.

It

is

hoped

that this

paper

will

stimulate

the

collection

of additional

test

data.

The

load-deflection relationships of

laterally

loaded

piles drivgri

into

Dohesive

soila

is similar to the

BtreBs-strain

relationships

as obtained

from

consolidated-

undr&ined

tests.

28

At

loads

less

than

one-half

to

one-third

the

Ultimate lateral

resistance of

the

pile,

the deflections increase

approximately

linearly

with the applied

load.

At

higher

load

levels,

the

load-deflection re -

iatlonshdps

become non-linear

and the

maximum

resistance

is

in general

Reached

when the deflection

at the

ground surface

Is

approximately

equal

to

ÿLQ%

of

the

diameter

or

side

of

the

pile.

The

ultimate

lateral

resistance

of

a pile

is

governed

by

either

the

yield

3-trength

of

the

pile

section

or

by the

ultimate

lateral

resistance

of

the sup¬

porting

soil.

It

will

be

assumed that

failure

takes

place by

transforming

the

'pile

into

a mechanism

through

the

formation

of

plastic hinges.

Thus the

same

principles

will

be

used

for

the

analysis

of

a

laterally loaded

pile

as for

a

Citatically indeterminate

member

or structure

and

it

will

be

assumed

that the

-moment

at

a

plastic

hinge

remains

constant

once

a

hinge

forms.

(A

plastic

hLnge

can

be

compared

to

an

ordinary

hinge with

a

constant

friction.)

The possible

modes

of

failure

of

laterally

loaded

piles

are

illustrated

in

Figs,

1

and

2 for

free

headed and

restrained

piles,

respectively.

An

unre¬

strained

pile,

which is

free

to

rotate around

Its

top

end,

Is

defined herein

as

On

free-

headed

pile.

Failure

of

a

free-headed

pili

(Fig.

1)

takes

place

wh

so

(a)

the

maximum

bending

moment

In

the

pile

exceeds

the

moment

causing

yielding

or

failure

of

the

pile

section,

or

(b )

the

resulting

lateral

earth pressures

exceed

the

lateral

resistance

of the

supporting soil

along

the

full length

of

the

pile

and

it

rotates

as

a

unit,

around

a

point

located

at

some

distance

below

the

ground

'

Surface

[Fig. 1(b)).

Consequently,

the

mode

of

failure

depends

on

the

pile

|

Langth, on

the stiffness

of

the

pile

section,

and

on the

load-

deformation

char¬

acteristics

of the

soil.

Failure caused

by the

formation

of a

plastic

hinge

at

the

section

of

maximum

bending

moment

[

Fig.

1(a)]

takes

place

when

the

pile

penetration

is

relatively large.

Failure

caused

by exceeding

the

bearing

Capacity

of

the surrounding

supporting soil

[Fig.

1(b)] takes place

when

the

Length

of

the

pile

and

Its

penetration

depth

are

small.

The

failure

modes

of

restrained

piles are

illustrated

in

Fig.

2.

Fixed-

keaded

piles

may

be

restrained

by

a

pile

cap

or

by

a

bracing

system,

as

is

frequently

the

case

for

bridge

piers

or for

off-shore

structures. In

the case

26

Wagner,

A.

A.,

Lateral

Load

Teats

on

Piles

fo r

Design

Information,

Symposium

n

Lateral

Load Tests on

Piles,

ABTM

Special Publication, Ho.

154,

1953,

pp. 59-72.

27

Walsenko,

A.,

Overturning

Properties

of

Short

Piles,

thesis

presented

to the

fniverslty of

Utah,

at

Salt

Lake,

Utah,

In

1958,

In

partial fulfilment

of

the

requirements

or

the

degree

0#

Master

of

Scleooe,

2-8

McClelland,

B.,

and

Fooht,

J.

A.,

Jr., Soil Modulus

for

Laterally

Loaded

Piles,

rans

actions,

A8CE,

Vol. 123,

1958, pp.

1049-1063.


5/37

SM2

PILE

RESISTANCE

31

when the

length

of

the piles

and

the penetration depths are

large,

failure

may

take

place when

two plastic

hinges

form

at the

locations

of

the

maximum

positive

and

maximum

negative

bending

moments.

The

maximum

positive

moment

is located

at

some depth

below

the

ground

surface,

while

the

maxi¬

mum

negative

moment is located

at

the

level

of

the

restraint

(at

the

bottom

of

a

pile

cap

or

at the

level

of

the

lower bracing

system

for

pile

bends).

For

truly

fixed-headed

conditions,

the

maximum

negative

moment

Is

larger

than

ths

maximum

positive moment and

hence,

the

yield

strength

of

the

pile

section

is

generally

exceeded

first

at

the

top of

the

pile. However,

the

pile

is still

able to resist

additional

lateral loads

after

formation

of

the

first

plastic

hinge

and

failure

does

not

take

place

until a

second

plastic

hiiige

romm

at

the

point

of maximum

positive

moment.

The

second hinge forms

when the

magnitude of this

moment

is

equal

to

the moment

causing

yielding

of

the

pile

section

I

Fig.

2(a)]

Failure

may

also take

place

after the formation

of

the

first

plastic

hinge

at

the

top

end of the

pile if

the lateral

soil

reactions exceed

the

bearing

ca¬

pacity of

the soil

along the

full

length

of

the

pile

as

shown

in

Fig.

2(b),

and

the

pile

rotates

around

a point

located

at Bome

depth

below

the

ground

sur¬

face.

The

mode

of

failure,

shown in

Fig. 2(b),

takes

place

at

intermediate

pile

lengths

and

intermediate

penetration

depths.

When

the

lengths

of the

piles

and the

penetration

depths are

small,

failure

takes

place when

the

ap¬

plied

lateral load exceedB

the resistance

of

the

supporting

soils,

as shown

in

Fig.

2(c).

In

this

case,

the action ofa

pile

can

be compared

to

that

of

a

dowel.

Methods

of computing

the distribution

of

bending

moments,

deflections

and

soils

reactions

at

working

loads

(at

one-half

to

one-third

the ultimate

lateral

resistance)

are reviewed in

the

following

section

and a

method for

the

calcu¬

lation

of the

ultimate

lateral

resistance of

free

and

restrained

piles

is

pre¬

sented

In a

succeeding

section.

Notation.

—

The

symbols

adopted for

use In

this

paper are

defined

where

they

first appear

and are arranged alphabetically

In

Appendix

I.

BEHAVIOR

AT

WORKING

LOADS

At

working

loads,

the

deflections of

a

single

pile

or

of

a

pile group

can

be

considered

to

increase

approximately

linearly

with

the

applied

load.

Part

of

the

lateral deflection

is

caused

by

the

shear

deformation

of the soil

at

the

time

of

loading

and

part

by

consolidation

and

creep

subsequent

to

loading.

(Creep

is

defined

as

the part of

the

shear

deformations

which

take place

after

loading.)

The

deformation caused by

consolidation

and

creep

increases

with

time.

It

will be

assumed

in

the

following

analysis,

that the

lateral

deflections

and the

distribution

of

bending

moments

and

shear forces

can be

calculated

at

working

loads by means of

the

theory

of

subfrade

reaction.

Thus,

It

will

be

assumed

that

the

unit

soli

reaction

p

(In

pounds

per

square

inch or

tons

per

square

foot)

acting

on

a

Laterally

loaded

pile

Increases In proportion

to

the

lateral

deflection

y.(ln

inches or

feet)

expressed by

the

equation

v&ctisfi)

p

ÿ

k

y U)

[

where

the

coefficient

k

(in

pounds

per

cubic

inch

or

tons

per

cubic

foot)

is

defined

as

the

coefficient

of

subgrade

reaction.

The

numerical

value of

the

I

}

i


6/37

c~<

to

-ft

J

VkW

( 0)

ILU

//

ÿo

M

(b )

ty

n

u

1

Wf

'/

I

I

i

i

V-.

waÿwss

:

n

ÿ»

//

//

/

/

(a )

1


7/37

SM 2

PILE

RESISTANCE

33

coefficient

of

sub

grade reaction

varies

with

the width

of

the

loaded

area

and

£1*9 load distribution,

as

well

as

with

the

distance

from

the

ground

sur£ace.29-33

The

corresponding

soil reaction per unit

length

Q

(In

pounds

per inch or

tons

per

foot)

can

be

evaluated

from

Q

«

k

D

y

(2)

in

which

D

is

the

diameter or

width

of the

laterally

loaded

pile.

If

k

D

is de¬

noted

K

(in

pounds

per

square

inch or

tons

per

square

foot), then

Q

«

K y

(3)

Methods for the

evaluation

of the

coefficient

K

for

pileB

driven

into

cohesive

soils

have been discussed

by

Terzaghlÿl

and

will

be summarized

subse¬

quently.

However,

the numerical value

of

this coefficient

is

affected

by

con¬

solidation and

creep.

In

the

following

analysis,

It

will be

assumed

that the

coefficient of

subgrado

reaction

is

constant

within

the

significant

depth.

(The

significant

depth

is

defined

as

the depth

wherein

a

change of the

subgrade

reaction

will

not affect

the lateral deflection

at the ground

surface

or the maximum

bending moment

by

more than

10%.)

However,

the

coefficient

of

subgrade

reaction

is

seldom

a

constant but

varies

frequently

as a

function

of

depth. It

will

be

shown

that

the

coefficient

of

subgrade

reaction

for

cohesive

soils

is

approximately

proportional

to

the

unconflned

compressive strength

of the

soil.

34

As

the unconflned compressive

strength

of

normally

consolidated

calys

and silts

Increases

approximately

linear

with depth,

the

coefficient

of subgrade

reaction can

be

expected

to

Increase

in

a

similar

manner as

Indicated

by

field

data

obtained

by

A. L.

ParracklO

and

by

Ralph

B.

Peck,

F.

ASCE

and

M.

T.

Davisson.21

The

uncon¬

flned

compressive

strength

of

overconsolldated

clayB

may

be

approximately

constant

with

depth

if ,

for

example,

the

overconsolldation

of

the

soil

has been

caused

by glaclation

while

the

unconflned

compressive

Btrengthmay

decrease

with

depth

if

the overconsolldation has been

caused by

desiccation.

Thus,

the

coefficient of

subgrade

reaction may,

for

an

overconsolldated

clay,

be

either

approximately

constant or

decrease

as

a function

of

depth.

Bo '

t, A.

M., Bending

of

an

Infinite

Beam

on

an

Elastic

Foundation,

Journal

of

Applied

Mecbanlca.

Vol. 4, No.

1,

A1-A7, 1937.

39

DeBeer,

E.

E.,

Computation

of

Beams

Resting

on

Soil,

Proceedings,

Second

Internatl.

Gonf.

on

Soil Mechstnioa and

Foundation Engrg.,

Vol.

1,

1948,

Rotterdam,

Hol¬

land,

pp.

119-121.

31

Terzaghi,

K.,

Evaluation of

Coefficients

of

Subgrade

Reaction,

*

Geo

technique,

London,

England,

Vol.

V,

1955,

pp.

297-326.

32

Veslc,

A.

B.,

Bending

of

Beams

Resting

on

Isotropic

Elastic

Solid,

Journal

of

the

Engineering

Mechanics

Division,

ASCE,

Vol.

87,

No. EM2,

Proc.

Paper

2800,

April,

1981,

pp.

35-51

33

Vealo, A.

B.t

Beams

on Elastic Subgrade

and

the

Winkler's Hypothesis,

Pro¬

ceedings,

Fifth Internstl.

Conf.

on

8oll

Mechanics

and

Foundation

Engrg.,

Vol.

I,

1961,

Paris,

France

pp.

845-850.

34

SJcempton,

A.

W.,

The Bearing

Capacity

of Clays,

Building

Research Congress,

London,

England

1951,

pp.

180-189.


8/37

March,

1964

SM

2

The

limitations

imposed on

the

proposed

analysis

by

the

assumption

of a

constant coefficient

o(

subgrade

reaction

can be

overcome. It

can

be

shown

+tat

the

lateral

deflections

can

be

predicted

at

the

ground

surface when the

Coefficient

of

subgrade reaction

increases

with

depth

If

this

coefficient

is

as

-

CMjmed

to

be

constant

and

If

its

numerical

value

is

taken

as

the

average

within

depth equal

to 0.8

/J

L.

Lateral

Deflections

.

—

For

the

case

when

the

coefficient

of

subgrade

reac-

f

}

r\r\ la

p/>natont

wlfli

/IavUK

tKjn

d

I

V>ii i-4

/ ri

o/

jv/1

ft

Ifin

woiidiriÿ

f

oments

and soil

reactions

can

be

calculated

numerically,

35,36,37

axialytl-

LAlly,30.3®

or

by means

of

models.

40

Solutions

are

also

available

for

the case

iJhen

a

laterally loaded

pile

has

been

driven

into

a

layered system consisting

;r

an

upper stiff crust

and

a

lower

layer

of soft

clays.

41

The

deflections,

bending moments and

soil

reactions

depend

primarily

on

the

dlmensionless

length

B

L,Ln

whÿch

B

Ls equal

to

ÿkD/4EpIp.ÿ

5-3 ®

In

this

expression,

Eplp

Is

the

stiffness

of

the

pile

section,

k the coefficient

of

a

sub-

sT'ade reaction,

and

D

the diameter

or

width

of

the laterally

loaded

pile.

A. B.

X/eslc,32 M.

ASCE

has

shown

that

the

coefficient

of

subgrade

reaction

can

be

'Valuated assuming

that the

pile

length

is

large

when

the dimenslonless length

Is

larger

than

2.25.

In

the

case

when the

dimenslonless

length of

the

pile

&L

Is

less

than

2,25,

the coefficient of

subgrade

reaction

depends

primarily

i?n.the

diameter

of the

test

plleÿand

on

the

penetration

depth.29,30,31

,32,33

It

can

be

shown

that lateral

deflection

yQ

at

the

ground

surface can be ex-

ffessed

as

a

function

of

the

dimensloidesB

quantity

yD

k

D

L/BÿThls

quantity

}; ,

plotted in

Fig.

3 as

a

function

of

the

dimenslonless pile length

ÿ

L ,

The

'c-teral

deflections

as

shown

in Fig.

3

have

been

calculated

for

the

two

cases

'>hen

the pile

is fully

free

or

fully

fixed

at

the

ground

surface. Frequently, the

laterally

loaded

pllels

only

partly

restrained

and

the

lateral

deflections

at

the

jvound

surface will

attain

values

between

those

corresponding

to fully

fixed

rd

fully

free conditions.

The

lateral deflections

at

the

ground

surface

can

be

calculated

for

a

free-

f\Jaaded

pile as can be seen from

Fig.

3

assuming

that

the

pile is

infinitely

jfcLff

when

the dimenslonless

length

B

L is less

than 1.5. For this

case, the

(literal

deflection

ls equal to:

4F

(1*1.5

£)

y

«

_

k

D

L

(4

a)

35

Qleser.S.M.,

Lateral Load

Testa

onVertlcal

Fixed-Head

and

Free-Head

Piles,

STM

Special

Publication,

no,

154,

1S53,

pp.

75-93.

30

Howe,

ft.

J.,

A

Numerical

Method

for

Predicting

the

Behavior of

Laterally

•*ided

Piling,

Shell

Oil

Co.,

TS

Memorandum

9,

Houston, Tex., May,

1955.

37

Ne-wmark,

N.

M., Numerical

Procedure for

Computing

Deflections,

Moments,

ui

Buckling

Loads,

Transactions,

ASCE, Vol. 108,

1943,

pp.

1161-1188.

38

Chang,

Y.

L.,

discussion

of

'Lateral Pile-Loading

Tests,

by

Lawrence

B. Feagin,

ransactlons,

ASCE,

Vol. 102,

1937, pp. 272-27-8.

Hetenyl,

M.,

Beams

on

Elastic

Foundation,

Unlv.

of

Michigan

PreaB, Ann

Arbor,

ich., 1946.

40

Thorns.

R.

L.,

A Model

Analysis

of a Laterally

Loaded

Pile, thesis

presented

to

e

University

of

Texas,

at

Auatin,

Tex., in 1957,

in

partial

fulfilment

of

the

requlre-

onts

for the degree

of

Master of

Science.

41

Davlsson, M.

T.,

and

QUI,

H.

L.,

Laterally

Loaded

Piles

In

a

Layered

System,

-ureal of the Soil

Mechanios

and

Foundations

Division.

ASCE,

Vol.

89,

No. 8M3,

Proc

-.per

3509,

May,

1&S3,

pp. *3-94.


9/37

&M

2

PILE

RESISTANCE

35

A

retrained

pile

with

a

dimexuaionleaa length

p

L

less

than 0.5

behaves

a*

an

Infinitely

a

tit?

pile

(Fig.

3)

and

the

lateral deflection at

the

ground

surface

can

be calculated

directly

from

the equation

k

D

L

(4b)

It

should

be r.cted

that

ar.

increase

of

ihe

pile

length

decreases

appreciably

the lateral

deflection

at the ground

surface fo r short

piles

(

ft

L less

than

1.5

and

0.5 for free-headed

and

restrained

piles,

respectively).

However,

a

change

of

the

pile

stiffness has

only

a

small

effect

on

the lateral deflection

for

such

plies.

The

lateral deflections

at

the

ground

surface

of

short

fixed

piles

are

theoretically

one-fourth

or

less

of

those

for the

corresponding

free-headed

piles

(Eqs.

4a

and

4b).

Thus,

the

provision

of

end

restraint

Is

an effective means

of

decreasing

the

lateral deflections

at

the

grourdjLurfÿtrff~or_aTRinglÿtÿai-ly_ÿoaded

pile.

This has

been

shown

clearlyÿbyÿfhe

tests

reported

by

G. A.

MbQammon,

F.

ASCE,

and

J.

C.

Aschepadan,

M.

ASCE.l®

These

tests

Indicate

that

the

lat¬

eral

deflection

of

a

free

pile

driven Into a soft

clay

deflected

at

the

same

lateral load

onthe-ayeragq

2.6

times

as

much

as

the corresponding

partially

restrained/pile.

The

lateral deflection*

at

the

ground

surface of

a

free-headed

pile

can be

calculated

assuming

that

the pile

La

infinitely long

(Fig.

3)

vrban

the

dlmen-

.

atonies*

length

p

L

exceeds

S.5.

For this case

(

p

L

larger

than

2.5)

the

lab

eral

deflection

can

be

computed

directly

from

-

2

P

Me

+

l)

k

D

in

which

koo

Is

thhÿaeffRient

of

subgrade

reactlofueOrrespondlng

to an

Infi¬

nitely

long

pile.

~~

—

~

-

A

restrained pilebehaves

as an

Infinitely

long pile

when the

dimension ess

length

p

L

exceeds 1.5

as

can be

seen

from

Fig.

3.

The corresponding

lateral

deflection

{p

L

larger

than

1.5)

can be

calculated

from

o

P

P

k

D

•O

(5b)

The lateral

deflections

at the ground

surface

depends

on

the

value

of

the

coefficient

of subgrade

reaction

within

the

critical depth.

This

depth can be

determined

from

the

following

considerations.

It can

be

seen

from

Fig.

3

that

the

lateral deflections

at

the ground

surface are approximately

10%

larger

than

those calculated

assuming that

the

pile

is

infinitely long

when

the

dlmen-

sionleBB

pile

length

or

embedment

length

p

L

la equal

to 2.0

and

1.0

for

re¬

strained

and

free-headed

plies,

respectively. Thus

the properties of

the

piles

or of the

soil

beyond

these dlmensionless depths

have

only

a

small effect

on

the

lateral

deflections

at

the

ground

Burface.

The

dlmensionlesB

depths

p

L

of 2.0 and

1.0

are therefore the

critical

depths

for

restrained

and

free-headed

piles, respectively.


10/37

Eq

(4o)

Eq

(4b)

ÿEq(5b)

DIMENS80NLESS LENGTH,

£L

FIG. 3.

-COHESIVE

SOILS—

LATERAL DEFLECTIONS

AT

GROUND

SURFACE

1

-t>

ÿacrÿ

(a )

AXIAL

AND LATERAL

LOADS

CO

c»

s

o

=r

M

CO

£

(b )

OVERTURNING

MOMENT

FIG.

4.

—

DISTRIBUTION

OF

SOIL REACTIONS

CO

3

to

MP


11/37

SM

2

PILE

RESISTANCE

37

Coefficient of

Sub

grade Reactionÿ-

the

following

analysis, the

coefficient

er f

subgrade reaction

has

been

computed

assuming

that

It

Is

equal

to

that erf

a

strip

founded

on the

surface

of

a

semi-infinite,

ideal

elastic

medium.

Thus,

it

has

been

assumed

that

the distribution

of

bending

moments,

shear

forces,

soil

reactions,

and deflections

are

the

same

for the

horizontal and

the vertical

members

shown in

Fig.

4.

However, the

actual

distribution

of

these

quantities

will

be

different

for

these

two

members

although

some

of

the

differences

tend

to

cancel each

other. For

example,

due to

edge

effects,

the coefficient

of sub-

grade

reaction

at

the head of the

vertical

member

will

be less

than

the

aver¬

age

coefficient

of

subgrade

reaction

for

the horizontal

member.

Furthermore,

,

since

the

vertical

member

is surrounded

on

all

sides

by

the

elastic

medium,

the

average

coefficient

of

lateral

subgrade

reaction

will

be

larger

than that

of the horizontal

member.

Thus, the deformations

at

the head

of

the

laterally

loaded vertical

members,

calculated

by

the

following

method,

are

only

ap¬

proximate

and can

be

used

only as an

estimate.

If

it

la required

to determine

the

lateral

deflections

accurately,

then

field

tests

are

required.

Long

Piles (/9

L

>

2.25ÿ

—

Vesic32,33

has

shown that

the

coefficient

of

sub-

grade

reaction,

k,

for

an

infinitely

long

strip with

the

width

D,

(such

as

a

wall

footing

founded

on

the

surface

of

a

semi-infinite,

Ideal

elastic

body)

is pro¬

portional

to

the

factor

a

and

the

coefficient

of

subgrade

reaction

Ko

for

a

square

plate,

with

the

length

equal to

unity.

The

coefficient

k„o

can

be

eval¬

uated from

a K

k

=

-=rÿ

(8)

«e

D

12

/KoD4

he

factor a

is equal to

0.52

-*/—

—

j—

where Ep

Ip

is

the

stiffness

of the

P

P

loaded

strip

or

plate.

In

the

following

analysis,

It

will

be

assumed

that

the

coefficient

of

lateral

subgrade

reaction can

be

calculated

from

Eq.

6 and

that

this

coefficient can

be

used

fo r the

determination

er f

the

distributionof bending

moments,

shear

forces

and

deflections

in

laterally

loaded piles.

Numerical

calculations

by

the

writer

have

indicated that

the

coefficient

a

can only

vary

between

narrow,

limits

for

steel,

concrete

or

timber

piles.

It

can

be

determined

approximately

from the

expression

a

-

nj

nj

(7)

in

which

ni

and

n2

are

functions erf

the uncooflned

compressive

strength

er f

the

supporting

soil

and

of

the

pile

material,

respectively,

as

indicated

in

Tables

1

and

2.

The

coefficient

a has

been

evaluated

for

steel

pipe

and

H-plles

as

well

as

for cast-ln-place or

precast concrete

piles

with cylindrical

ctosb

sections.

The minimum value of 0.29

was

calculated

for

steel

H-plles

driven

into

a

very

soft

clay

and loaded

in

the

direction

of

their

largest

moment

re¬

sistance.

The

maximum

value

of

0.54

was calculated

for

timber

piles

driven

into

very

stiff

clays,

As

an

example, the

factor

a

Is

equal

to

0.36

(

1.00

x0.36)

as

calculated

from

Eq.

7 for

a

50

ft

long

steel

pipe

pile

driven

Into

a

clay

with an uncon-


12/37

March,

1964

SM

2

ned

compressive

strength

of

1.0 ton

per

»q

ft . The

corresponding

coefficient

'

subgrade

reaction

La

equal

to

18.0

('0.36

X

50)

tons per

»q

ft when the

co-

ficient

Kq

is

equal to

50

tons

per

»q

ft

The coefficient

K0

corresponds

to

•

o

coefficient

of

subgrade

reaction of

a

plate with

a

diameter

of 1.0 ft

The

coefficient

er f

subgrade

reaction

increases

frequently

with

depth.

Cal-

ÿ

1niinna

tetrA

{

»-wi ino

*

4

1

at

A»a

I

/lAfl

«ytf(nna

nor*

Kn

nfllnnlo

f

fVÿ

I

r If 4a

umlOiLD

iiatc

ijiutvKiTU

i»wÿ

uso

taiQXJU

ucmwÿkivii v»ui

xro

nuvmsvoM

c*

it

id

isumed

that

the

coefficient

of

subgrade

reaction

is

a

constant

and

that

its

imerical

value

la

equal

to

that

corresponding

to the

dimeneionless

depth

0

L

0.4.

For

the

case

when

the

coefficient of

subgrade

reaction

decreases

with

ptb,

the

method

developed

by Darisson

and H. L. Gill,

41

A.

M.

ASCE can

ri

used.

For

long

piles, the

calculated

lateral

deflections

are insensitive

to

the

as-

umed vaiue

cf

the

coefficient

of Bubgrade

reaction.

If ,

for example,

the

co-

TABLE

1.

-EVALUATION

OF

THE

COEFFICIENT

ny

(EQ.

7)

Unconfined

Compressive

Strength

cÿ,

tone

per

square

foot

Coefficient

nj

Leas

than

0.5

0.32

0.5

to

2.0

0.36

Larger than 2.0

0.40

TABLE

2.

-EVALUATION

OK

TILE

COEFFICIENT

n3

(EQ.

7)

Pile

Material

Coefflolent

n2

Steel

1.00

Cooorete

1.15

Wood

1.30

'ficient cf

Bubgrade reaction is

half

the assumed

value,

then the

deflections

t

the

ground

surface

will

exceed the

calculated deflections

by about

20%.

As

r

esult,

it

is,

in

general,

sufficient

to

estimate the

magnitude of

the

coeffi-

ient

of

subgrade

reaction.

Short

Piles

(0

L

<

2.25).—

The

coefficient

of

subgrade reaction

for

later-

1

ly

loaded

short

piles

with

a

length

0

L

less

than 2.25

may

be

calculated ap-

roxlmately

by the following

method.

Short

piles will

behave

under

lateral

load

as

If they

are

infinitely

stiff and

lateral

load

P

acting at

mid-height

will

cause

a

pure

translation of

the pile

i Bhown

in

Fig.

5(a)

.

A

moment

M acting

at

mid-height

of

the

pile

will result

i

a pure

rotation

with

respect to

the

center

of

the

pile

and

the

distribution

of

teral

earth

pressures

will

be

approximately

triangular

as

shown

In

Fig.

5(b)

isBumtng

a

constant

coefficient

of

subgrade

reaction).

It

should

be

noticed

iat amy

force

system

acting on

a

pile can

be

resolved

into

a

Bingle

lateral

ÿ

rce

and

a

moment

acting at

the

center of

the embedded

section

of the

loaded


13/37

7W7H

ÿ

L*.

r

i

U

ASSUMED

I

4

ACTUAL

\

y

(o )

TRANSLATION SOIL REACTION

»JV


14/37


15/37


16/37

\

42

March,

1964

SM

2

ficlent

will

b#

overestimated

ii

the

shearing

strength

and

the

soil modulus

decrease

with

depth.

Remolding of the

soil

(as

a result

of

pile

driving)

cause

a

decrease of

the

LnitLal

modulus

and

the

secant

modulus

to a

distance

of

approximately

one

pile

diameter

from

the

surface

of

the

pile.

Consolidation on

the

other hand

causes

a

substantial

increase

with

time

of

the

shearing

strength,

of

the

initial

and

of

the

secant

moduli

for

normally

or

lightly

overconsolldated

clays.

Hcrw-

»v?r ,

the

hearhw

strength

and the

secant

modulus

for

heavily

overconsoli-

dated

clays

may

decrease

with

time.

The

deflections

at

working

loads

(approximately

one-half to

one-third

the

ultimate

bearing

capacity)

are

proportional

to the

secant modulus

of

the so

11ÿ

when

the modulus

is determined at

loads

corresponding

to

between one-half

and

one-third

the

ultimate

strength

of

the

soil.

34

This

secant

modulus

may be

considerably less

than

the

Initial

tangent modulus

of

elasticity

of

the

soil.

45

In

the

following

analysis,

the

secant

modulus

E50

corresponding

to

half

the

ultimate

strength

of

the

soil will be

assumed

to

govern

the

lateral

deflections

at

working

loads.

(The

assumption

has

been made

also

by

A.

W.

Skempton34

In the

analysis

of the initial

deflections

of spread

footings

founded at or

close

to

the ground

surface.)

The

deflection

do

of a

circular

plate

can

then be

cal¬

culated

from the

equationÿ

0.8

B

q

(l

-

u

2

d

(9)

°

50

In

which

B Is

the

diameter

of the loaded

area,

q

denotes the

Intensity

of the

applied load

andM«

refers

to

Poiason's

ratio.

Since

q/do is

equal

to the coef¬

ficient

of

subgrade

reaction

Icq,

It can

be

seen

that

the

coefficient

of

subgrade

reaction

is

indirectly

proportional

to

the

diameter

of

B

of

the loaded

area.

If

IcqB is defined

as

Ko

and the

Poiason's

ratio

is taken

as

0.5,

then

K

=

1.67

EKn

(10)

o

50

Skempton34

has

found that the

secant

modulus

E50

is

approximately

equal

to 25

to

100 times

the

unconfmed


of

a cohesive

soli.

Analysis

of

test data

reported

by

Peck and

Davissonÿl

on the

behavior

of

a

laterally

loaded H-pile driven

into a normally

consolidated,

highly

organic

silt

indicates,

at the

maximum applied

load,

that

the

secant

modulus

load

Is

approximately

equal to 100 times the

cohesive

strength

as

measured

by

field

vane

tests

(50

times

the

uncoftfined compressive strength of the

soil).

Using

a

value

of

E50

equal

to 25

to

100

times the

unconfined compressive

strength,

the

coefficient

Kq

can

be

expressed

in terms

of the

unconfined

com¬

pressive

qu

(Eq.

10)

as

K

-

(40

-

160)

qÿ

(11)

45

Terraghl,

K., and

Peck,

R.

B-,

Soli

Meohantc*

In

Engineering

Praotloe,

John

Wiley

L

Sons,

Inc.,

New York,

N.

Y.,

1&48.


17/37


18/37

44

March,

19&4

SM

2

Consolidation

and creep

cause

an

increase

in lateral deflections

of

short

piles

(/3

L

less

than

1.5

and

0.5

for free-headed

and

restrained

piles,

respec¬

tively)

which

is

inversely

proportional

to the

decrease

in

the coefficient

of

lateral

sub

grade

reaction

as

indicated

by Eqs.

4a

and

4b.

A decrease

of

this

coefficient,

for

example,

to

one-third

its

initial

value

will

cause

an

Increajse

of

the

initial

lateral

deflections

at

the

ground surface

by

a factor

of

three.

In

the

case

of

a

long

pile

(j3

L

larger

than

2.5

and

1.5

for a free-headed and

a

restrained

pile,

respectively)

the

increase

of

lateral

deflection

(Eqs.

5a

and

5b)

caused

by

consolidation

and

creep

is less

than

that

of

a

short pile.

The

increase in

lateral

deflections

caused

by

consolidation may

also

be

calculated

bv means

of

a

settlement

analysis

based

on

the

assumption

that

the

distribution

of soil reactions

along

the

laterally

loaded piles

is governed

by

a

reduced

coefficient

of

lateral

soil

reaction,

that

the

distribution

of

the

soil

pressure

within the soil

located

In

front

of

the

laterally

loaded pile can be

calculated,

for

example,

by

the

2:1

method

or

by

any

other suitable

method

and

that

the

compressibility

of the

aoilcanbe

evaluated

by consolidation tests

or

from

empirical relationships.

(The

2:1

method

assumes that

the

applied

load

Is distributed over

an

area which

Increases In proportion to the

distance

to the applied

load.

This

method

closely

approximates

the stress

distribution

calculated

by

the theory of

elasticity

along the

axis

of

loading.)

Because

these

proposed

methods

of

calculating

lateral

deflections

have

not

been

substantiated

by

test

data

they

should

be

used

with

caution.

Comparison

xoith

Test

Data.

—

The

lateral deflections at

working

loads

can

be

calculated

by the

hypothesis

previously

presented

if

the

stiffness of

the

pile

section,

the

pile

diameter,

the

penetration

depth,

and the

average

uncon-

flned

compressive

strength

of

the

soil

are

known

within the

significant

depth.

Frequently

only

fragmentary

data

concerning

the strength

properties

of

the

supporting

soil are

available.

The

lateral

deflections

calculated

from

EqB.

4a,

4b,

5a

and 5b

have

been

compared

In

Table

4

with

test data

reported

by

W.

L.

Shilts, F.

ASCE, L.

D.

Graves,

F.

ASCE

and

C. G.

DriBCOll,24

by

Parrack,19 by

J. F.

McNulty.lf

F.

ASCE,

by

J.

O.

Osterberg,18

F.

ASCE,

and

by

Peck and

Davisson.21

In

the

analysis

of

these test

data,

it has.

been

assumed

that

the moduli of

elasticity

for

the pile

materials

wood,

concrete

and steel are

1.5

x

10®,

3 x 10 ®

and

30

x

106 psl,

respectively,

and that the

ratio Eso/qu

is

equal to

50.

The test

data

are

examined

in detail

in Appendix

n.

It

can

be

seen

from

Table 4

that

the

measured

lateral

deflections

at the

ground

surface

varied between

0.5 to

3.0

times the calculated

deflections.

It should

be

noted that

the calculated

lateral

deflections are for

short

piles

Inversely proportional

to

the

assumed

coefficient

of

subgrade

reactions

and

thus

to

the

measured

average

unconfined


of

the support¬

ing

soil.

Thus

Bmall variations of

the

measured

average

unconfined

compres¬

sive strength

will

have

large

effects

on the calculated

lateral

deflections.

It

should also

be

noted

that

the

agreement

between

measured

and calculated

lateral

deflections

improves

with

decreasing

shearing

strength

of

the

soil.

The cohesive

soils

reported

with a

highunconfined

compressive

strength

have.

been

preloaded

by

desiccation

and

it

is

well

known

that the

shearing

strength

of

such

soilB

Is

erratic

and

may vary

appreciably

within short distances

due

to the

presence

of

shrinkage

cracks.

The

test

data

indicate

that

the

proposed

method

can be used to

calculate

the

lateral

deflections at

working

loads

(at

load

levels

equal to

one-half

or


19/37

SM

2

PILE RESISTANCE

45

TABLE

4.

-LATERAL

DEFLECTIONS

Pile

Teat

(1)

Pile

D,

In

feet

(2)

Eccen-

trio

ity

e, in

feet

(3)

Depth

of

Embed¬

ment

L ,

in

fee4

{*)

Applied

load

P,

in

klpe

(5)

Average

Unconfined

Hrtrn

I

y-

Strength

cÿ,

ln

tone

per

Bq

ft

(6)

Measured

Lateral

DeOectloo

ytesb

in

Inches

(7)

Shllts,

Oravee

and DrlscoU,24 1948

Calculated

Lateral

Deflection

yoalc

In

lnchea

(8)

itauo

yteatÿyoalo

(9)

9» 1.17

9.0

6.5

2.1

0.95 0.35

2.71

10

2.0

10.0

5.0

2.0 1.53 0.40

0.34

1.18

14

2.0

10.0

6.0

3.0 0.20 0.42

0.48

Parraclt,19

1952

1

2.0

_b

75.0

20

0.37

0.098

0.107

0.92

40

0.214

0.219

0.98

60

0.418

0.324

1.29

80

0.656

0.428

1.53

McNuJty.n

1956

A

1.0

_b

50.0

5

1.20C

0.05

0.15

0.33

10

0.21 0.29 0.72

15

0.50

0.44

1.13

.

20

0.86

0.58

1.48

B

1.0

_b

50.0

'

5

1.20C

0.08 0.15

0.53

10

0.27

0.29

1.04

.15

0.57

0.44

1.29

20

0.95

0.58

1.63

Oaterberg,

1

8

1958

T1

0.90 15.0 6.00

2.BI

2.22

0.82

0.400

2.07

T2 0.

HO

15.0 6.00

2.42

2.22 1.25

0.333

3.75

T3

0.90

15.0

4.00 1.42

2.22

0.71

0.324

2.19

T4

0.90

15.0 4.00

1.42

2.22

0.71

0.324

2.19

T5

0.B0 15.0

7.79

4.00

2.22

0.83

0.501

1.66

T6

0.90

15.0 9.50

3.91 2.64

0.42

0.272 1.55

T7

0.90 15.0

5.84

2.91

2.37

1.07

0.385

2.97

T8

1.50

15.0

6.00 4.87

1.84

0.53

0.601

0.88

T»

2.00

15.0 6.00

5.81

2.40

0.25 0.466

0.54

T10

2.00

15.0

6.00

4.87

3.03

0.37

0.311

1.19

T il

2.67

14.0

6.00

9.78

3.05

0.32

0.489

0.65

T12

3.09

13.2

6.00 12.75

3.05

0.49

0.471

1.07

rrt 9

1.50

15.0

6.00

6.27

2.25 0.77

0.535

1.44

T14

0.90

15.0

6.16

3.41 3.05

0.94

0.326

3.09

Peck

and

Davisson,21 1962

1

H-plle

32.5

64.3

1.0

0.400d

0.6

0.63

0.95

(14BD89)

1.5

1.4

0.94

1.49

2.0

1.7

1.26

1.36

2.5

2.5

1.58

1.58

3.0

3.5

1.89 1.85

a

In

contact

with

remolded soil

b

Pile

restrained

0

Estimated

from

standard

penetration teet

d

Calculated from field

vane

tests


20/37

40

March,

19&4

ÿ

SM 2

one-third

the

ultimate

lateral

capacity

of

a

pile)

when

the

unconflned

com¬

pressive

strength

of

the

soil

is

less

than about

1.0

ton

per

sq

ft. However,

when

the

unconflned

compressive

strength

of the

soil

exceeds

about

1.0

ton

per sq

ft,

it

is

expected

that

the

actual

deflections at

the

ground

surface

may

be

considerably

larger

than

the

calculated

lateral deflections

due

to

the er¬

ratic

nature

of

the

supporting

soil.

However,

It should be

noted

also

that

only

an

estimate

of

the

lateral

de¬

flections

is

required

for most

problems

and

that

the accuracy of the

proposed

method

of

analysis la probably

sufficient

for this

purpose.

Additional

test

data

are

required

before

the

accuracy and

the

limitations

of the

proposed

method

can

be

established.

ULTIMATE

LATERAL

RESISTANCE

General.—

At

low

load

levels, the

deflections

of

a

laterally

loaded

pile

or

pole increase approximately linearly

with the

applied

load.

As

the

ultimate

capacity

is

approached,

the lateral

deflections

Increase

very

rapidly

with

increasing

applied

load.

Failure

of

free

or

fixed-headed

plies

may

take

place

by

any of

the

failure

mechanisms

shown in

Figs.

1 and

2.

These

failure

modes

are

discussed

below.

Unrestrained Piles.—

The failure

mechanism

and the

resulting

distribution

of lateral

earth

pressures

along a

laterally

loaded free-headed

pile

driven

into

a cohesive soil is

shown

in

Fig.

7.

The

soil

located

in

front

of

the

loaded

pile

cloBe

to the

ground

surface moves upwards

in

the

direction of

least

re¬

sistance,

while

the

soli

located

at

some

depth

below

the

ground

surface

moves

in

a

lateral direction

from

the

front to

the back

side of the

pile.

Furthermore,

It

has

been observed

that

the

soil

separates

from

the

pile

on

Its

back

side

down

to a

certain

depth

below

the ground

surface.

J.

Brlnch-Hansen47

has

shown

that

the

ultimate

soil

reaction

against

a

laterally

loaded

pile

driven

into

a cohesive

material

(baaed

on the assumption

|

that

the

shape

of

a

circular section

can

be

approximated by

that

of

a

square)

varies

between

8.3cu

and

11.4cu,

where

the

cohesive

strength

cu

la

equal

to

half the

unconflned

compressive

strength

of

the

soil.

On

the other

hand,

L.

C.

Reese,

48

M.

ASCE has

Indicated

that

the

ultimate

soil

reaction increases

at

failure

from approximately

2

cu

at

the

ground

surface

to

12cu

at a

depth

of

approximately three

pile

diameters

below

the

ground

surface.

T.

R.

McKen-

zleÿ9

has

found

from

experiments

that

the

maximum

lateral

resistance

is

equal

to

approximately

8

cU('

while

A. G.

DastidarSO

used

a

value

of

8.5

Cu

when

calculating

the

restraining

effects of

piles

driven

into

a

cohesive

soil.

The

ultimate

lateral

resistance

has

been calculated in

Appendix

III

as

a

func¬

tion of the

shape

at

the

croBS-sectional

area

and

the

roughness

of

the pile

47

Brlnch-Hansen,

J. ,

The

Stabilizing

Effect

of Pilea

In CLay,

C.

N.

Poat,

Novem¬

ber,

1948.

(Published

by Christian

L

Nielsen,

Copenhagen, Denmark).

48

ReeBe,

L.

C., dlBCUBslon

at

Soil

Modulus

for

Laterally

Loaded

Piles,

by B.

Mc-

Clelland

and

J. A.

Focht,

Jr.,

Trails

actions,

ASCE,

Vol.

123, 1958, pp.

1071-1074.

49

McKenzle, T.

R.,

Strength of

Deadman

Anchora

In

Clay, thesis

presented

to

Princeton

University,

at

Princeton,

N. J.,

In

1955,

In

partial

fulfilment of

the

require¬

ments

for

the

degree

of

Mastsr:of

Science.

80

Dastldar,

A.

O.,

Pilot

Teb'ta

to

Determine

the

Effect

of

Piles

In

Restraining

Shear

Failure

In

Clay,

Princeton Unlv.,

Princeton, N.

J.,

1956

(unpublished).


21/37

KM

2

PILE

RESISTANCE

47

surface.

The

calculated

ultimate

lateral

resistances varied

between

8,28

cu

and

12,56

cu

as can

be seen

from Table

5.

Repetitive

loads,

such

as

those

caused

by

wave

forces,

cause

a

gradual

decrease of the

shear

strength

of the soil

located

in

the

immediate

vicinity

of the

loaded

pile. The

applied

lateral load

may

cause,

in

the

case

where

the

soil

is over-

consolidated,

a decrease of

the pore

pressures

and

as

a

result,

gradual

swelling

and

loss in

shear

strength

may

take

place

as

water

Is

ab¬

sorbed from

any

available source.

Unpublished

data

collected

by the

author

suggest

that

repetitive

loading could

decrease

the ultimate

lateral resistance

of

the

soil about

one-half

Its

Initialvalue. Additional

data

are

however

requited.

LATERAL

APPROXIMATELY 3D

OAD,

P

*07

m

SOIL

MOVEMENTS

1.5

0

8 TO

12

Cy

D

(a )

DEFLECTIONS

(b)

PROBABLE

(c )

ASSUMED

DISTRIBUTION

DISTRIBUTION OF

OF

SOIL

REACTIONS

SOIL

REACTIONS

FlO.

7.

-DISTRIBUTION

OF

LATERAL

EARTH

PRESSURES

The

ultimate

lateral resistance of

a

pile

group

may

be

considerably

less

than

the

ultimate lateral

resistance

calculated

as

the

sum

of

the

ultimate

resistances of

the individual

piles.

N.

C. Donovan,

51

A.

M.

ASCE found

no

reduction

In

lateral

resistance

when

the

pile

spacing

exceeded

four

pile

di¬

ameters.

When the piles were

closer

than

approximately

two pile

diameters,

the

piles

and

the soil located

within the

pile group

behaved

as

a

unit.

51

Donovan,

N.

C.,

'Analysis

of Pile Oroups,

thesis

presented

to

Ohio

State

Univer¬

sity, at

Columbus,

Ohio,

In 1959,

In

partial

fulfilment of

the requirements

for the

degree

of

Doctor

of Philosophy.

1


22/37

48 March,

1964 SM

2

The

probable distribution

of

lateral

soil

reactions is shown In

Fig.

7(b).

On

the

basis

of

the

measured

arid

calculated

lateral

resistances,

the probable

distribution has

been

approximated

by

the

rectangular

distribution

shown

in

Fig.

7(c).

It

has

been

assumed that

the

lateral

soil

reaction is

equal

to

zero

to

a

depth of

1-1/2

pile

diameters

and equal to 9.0

c\iD

below

this

depth. The

resulting

calculated

maximum bending moment

and

required

penetration

depth

(assuming

the

rectangular

distribution

of

lateral

earth

pressures

shown

In

Fig.

7c)

will

be

somewhat

Larger

than

that

corresponding

to the

probable

pressure

distribution

at

failure.

Thus

the assumed

pressure

distribution will

yield

results

which

are

on tire

safe side.

Short Piles.—

The

distribution

of

soil

reactions

and

bending

moments

along

a relatively

short

pile at

failure

Ls shown

in

Fig.

8.

Failure

takes

place

when

the soil

yields

along

the

total-

length

of the pile,

and

the

pile

rotates

as

a

unit

M

cuD

max

FIO. 8.

-DEFLECTION,

SOIL

REACTION

AND

BENDING

MOMENT

DISTRIBUTION

FOR A

SHORT

FREE-

HEADED PILE

arouna

a

promt

located

at

some

depth

below

the

ground

surface.

The

maximum

moment

occurs

at

the

level

where

the

total

shear

force

in

the

pile

is

equal

to

zero

at a

depth

(I

+

1.5

D)

below

the

ground

surface.

The distance

f

and the

maximum

bending

moment M*108

can

then

be

calculated from the two

equations:

f =

9

c

D

u

(12)

and

f


23/37

8M 2 PILE

RESISTANCE

49

Mÿ09

»

P

(e

+

I.5D

+

0.5f)

max

(13)

in which

e

is

the

eccentricity

of

the

applied

load as

defined

In

Fig.

8.

The

J,

part of

the

pile

with

the length

g

(located

below the

point of maximum

bending

TABLE

5.

-ULTIMATE

LATERAL

RESISTANCE

SLIP

FIELD

PATTERN

SURFACE

ULTIMATE

LATERAL

RESISTANCE,

q

u/c..

utt

u

ROUGH

12.56

ROUGH 11.42

SMOOTH 11.42

SMOOTH 9.14

SMOOTH

8.28

moment)

resists the bending

moment

Then

from

equilibrium

require¬

ments

Mÿ8

=

2.25

D

g2

max

(14)

The

ultimate

lateral

resistance

of

a

short

pile

driven

into

a

cohesive

soli

can then

finally

be

calculated

from

Eqs.

12,

13 and

14 if it

is

observed

that


24/37

50

March,

1964

8M 2

L

-

(1.5

D +

f +

g)

.

.....

15)

The

ultimate

lateral

resistance

can also

be

determined

directly

from

Fig.

9

where

the

dimeaslonless

ultimate

lateral

resistance

Pult/Cuÿ

has

been

plot¬

ted a=

a

function

of

the

dimsasionless

embedment

length

L/D.

It

should be

emphasized that

it

has been

assumed

in this

analysis

that

failure

takes place

when

the

pile

rotates

as

a

unit,

and

that the

corresponding

maximum bending

moment calculated

from

Eqs.

13

and

14

la less

than

the

ultimate or

max

yield

moment

resistance

of the pile

section

Myield-

.hVrTJ.

.

'

r

r

/r

/

RESTRAINED

«

40

FREE-HEADED

l

O

4

8

12

EMBEDMENT

LENGTH,

L/D

710.

9.—

COHESIVE

SOILS-

[bengt b. broms] lateral resistance of pile

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